A formal solvability of a coupling equation for PDEs of Briot-Bouquet type (Microlocal analysis and asymptotic analysis)

Abstract

We study couplings for a pair of a partial differential equation of Briot-Bouquet type in the t variable and its model equation, without assuming the analytic dependency in t. In this report, we concentrate on the formal solvability --the existence of a formal solution of a special form-- of a coupling equation on one side indicated as (Psi). The precise statement concerning the convergence, together with a similar question on the reversed equation, that is, the coupling equation on the other side indicated as (Phi), will be published elsewhere.